Toward ecologically explicit null models of nestedness

A community is "nested" when species assemblages in less rich sites form nonrandom subsets of those at richer sites. Conventional null models used to test for statistically nonrandom nestedness are under- or over-restrictive because they do not sufficiently isolate ecological processes of interest, which hinders ecological inference. We propose a class of null models that are ecologically explicit and interpretable. Expected values of species richness and incidence, rather than observed values, are used to create random presence-absence matrices for hypothesis testing. In our examples, based on six datasets, expected values were derived either by using an individually based random placement model or by fitting empirical models to richness data as a function of environmental covariates. We describe an algorithm for constructing unbiased null matrices, which permitted valid testing of our null models. Our approach avoids the problem of building too much structure into the null model, and enabled us to explicitly test whether observed communities were more nested than would be expected for a system structured solely by species-abundance and species-area or similar relationships. We argue that this test or similar tests are better determinants of whether a system is truly nested; a nested system should contain unique pattern not already predicted by more fundamental ecological principles such as species-area relationships. Most species assemblages we studied were not nested under these null models. Our results suggest that nestedness, beyond that which is explained by passive sampling processes, may not be as widespread as currently believed. These findings may help to improve the utility of nestedness as an ecological concept and conservation tool.     

Temporal variability of nestedness and idiosyncratic species in stream insect assemblages

Aims The nested subset pattern has been widely studied in the last 20 years, and recent syntheses have challenged the prevalence of this pattern in nature. We examined the degree of nestedness, its temporal variability and its environmental correlates in stream insects of a boreal drainage system. We also examined differences between nested and idiosyncratic species in site occupancy, niche position and niche breadth. Location Koutajoki drainage basin in northern Finland. Methods We used (i) nestedness analyses with three null models for testing the significance of nestedness; (ii) Spearman rank correlation to examine the correlates of nestedness; (iii) outlying mean index analysis to analyse the niche characteristics of species; (iv) and t‐test to examine differences in niche breadth, niche position and site occupancy of idiosyncratic and other nested species. Results Stream insect assemblages were significantly nested in each of the three study years. The maximally packed matrices were significantly nested according to the nestedness calculator based on null models I (species frequencies and site richness equiprobable) and II (species frequencies fixed and site richness equiprobable), but non‐significant based on a conservative null model III (species frequencies and site richness fixed to those of the observed matrix). The most important correlate of nestedness was stream size, whereas isolation, productivity (total phosphorus) and habitat heterogeneity exhibited non‐significant relationship with nestedness. Idiosyncratic species occurred, on average, at more sites than nested species, mirroring the restricted distributions of several nested species that were inclined towards species‐rich sites. Idiosyncratic and nested species also differed in niche position and niche breadth, with idiosyncratic species having, on average, less marginal niche positions and wider niches than nested species. Main conclusions Stream size correlated with nestedness, possibly because small streams were inhabited only by species able to persist under, or colonize shortly after, disturbances, while most species could occur at larger sites where disturbances are less severe. From the conservation perspective, our findings suggest that stream size really matters, given that sites with high species richness and many rare species are more likely to occur in larger streams. However, also the requirements of idiosyncratic species should be accommodated in conservation planning.     

Nested bird and micro-habitat assemblages in a peatland archipelago

Biotic assemblages of insular habitats are nested when poor assemblages are subsets of richer ones. Nestedness of species assemblages is frequent and may result from selective extinction or frequent colonization in insular habitats. It may also be created by a nested distribution of habitats among islands or by sampling bias. We sampled 67 isolated peatlands (7–843 ha) in southern Quebec, Canada, to measure nestedness of bird species assemblages among peatlands and assess the habitat nestedness hypothesis. Species and microhabitat assemblages were both strongly nested among peatlands. Whether sites were ranked by species richness, microhabitat richness or peatland area had no effect on nestedness. However, microhabitat nestedness was significantly reduced when sites were sorted by area rather than by microhabitat richness. As expected, if bird-microhabitat associations are responsible for the nested pattern of distribution, we found a positive correlation between the contributions of bird species and microhabitats to individual site nestedness. Nevertheless, microhabitat assemblages were significantly less nested than bird species assemblages, possibly because of frequent recolonization by birds or uneven sampling among sites. Received: 12 June 1998 / Accepted: 20 September 1998     

A protocol to compare nestedness among submatrices

Searching for nestedness has become a popular exercise in community ecology. Significance of a nestedness index is usually evaluated using z values, and finding that a matrix is nested is typically a common result. However, nestedness is not likely to be spread uniformly within a matrix of species presence/absence per site. Selected parts of the matrix may show a degree of nestedness significantly higher (or lower) than expected from the overall pattern. Here we describe a procedure to assess if a particular submatrix (i.e., a peculiar combination of rows and columns extracted from the complete matrix) is more or less nested than expected for an assortment of sites and species taken at random from the same overall matrix. The idea is to obtain several submatrices of different sizes from the same overall matrix and to calculate their z values. A regression is then performed between z values of submatrices and their sizes. A nestedness index independent of matrix size is suggested as the deviation of the z value of a particular submatrix from that expected according to the regression line. We applied our protocol to 55 matrices with different nestedness indices under various null-models and, for purpose of demonstration, we discussed in detail a single case study regarding various animal groups of the Aegean Islands (Greece). The obtained results strongly encourage further research to focus not only on the question whether a matrix is nested or not, but also on where and why nestedness is confined.     

Disentangling community patterns of nestedness and species co-occurrence

Two opposing patterns of meta‐community organization are nestedness and negative species co‐occurrence. Both patterns can be quantified with metrics that are applied to presence‐absence matrices and tested with null model analysis. Previous meta‐analyses have given conflicting results, with the same set of matrices apparently showing high nestedness (Wright et al. 1998) and negative species co‐occurrence (Gotelli and McCabe 2002). We clarified the relationship between nestedness and co‐occurrence by creating random matrices, altering them systematically to increase or decrease the degree of nestedness or co‐occurrence, and then testing the resulting patterns with null models. Species co‐occurrence is related to the degree of nestedness, but the sign of the relationship depends on how the test matrices were created. Low‐fill matrices created by simple, uniform sampling generate negative correlations between nestedness and co‐occurrence: negative species co‐occurrence is associated with disordered matrices. However, high‐fill matrices created by passive sampling generate the opposite pattern: negative species co‐occurrence is associated with highly nested matrices. The patterns depend on which index of species co‐occurrence is used, and they are not symmetric: systematic changes in the co‐occurrence structure of a matrix are only weakly associated with changes in the pattern of nestedness. In all analyses, the fixed‐fixed null model that preserves matrix row and column totals has lower type I and type II error probabilities than an equiprobable null model that relaxes row and column totals. The latter model is part of the popular nestedness temperature calculator, which detects nestedness too frequently in random matrices (type I statistical error). When compared to a valid null model, a matrix with negative species co‐occurrence may be either highly nested or disordered, depending on the biological processes that determine row totals (number of species occurrences) and column totals (number of species per site).     

Inferences about nested subsets structure when not all species are detected

Comparisons of species composition among isolated ecological communities of different size have often provided evidence that the species in communities with lower species richness form nested subsets of the species in larger communities. In the vast majority of studies, the question of nested subsets has been addressed using information on presence‐absence, where a “0” is interpreted as the absence of a given species from a given location. Most of the methodological discussion in earlier studies investigating nestedness concerns the approach to generation of model‐based matrices corresponding to the null hypothesis of a nonnested pattern. However, it is most likely that in many situations investigators cannot detect all the species present in the location sampled. The possibility that zeros in incidence matrices reflect nondetection rather than absence of species has not been considered in studies addressing nested subsets, even though the position of zeros in these matrices forms the basis of earlier inference methods. These sampling artifacts are likely to lead to erroneous conclusions about both variation over space in species richness, and the degree of similarity of the various locations. Here we propose an approach to investigation of nestedness, based on statistical inference methods explicitly incorporating species detection probability, that take into account the probabilistic nature of the sampling process. We use presence‐absence data collected under Pollock's robust capture‐recapture design, and resort to an estimator of species richness originally developed for closed populations to assess the proportion of species shared by different locations. We develop testable predictions corresponding to the null hypothesis of a nonnested pattern, and an alternative hypothesis of perfect nestedness. We also present an index for assessing the degree of nestedness of a system of ecological communities. We illustrate our approach using avian data from the North American Breeding Bird Survey collected in Florida Keys.     

Nestedness and niche‐based species loss in moorland plant communities

Communities in isolated habitat patches surrounded by inhospitable matrices often form a nested subset pattern. However, the underlying causal mechanisms and conservation implications of nestedness in regional communities remain controversial. The nested ranks of species in a nested species‐by‐site matrix may reflect a gradient of species vulnerability to extinction or of colonization ability. However, nestedness analysis has rarely been used to explore determinants of species rank; consequently, little is known of underpinning mechanisms. In this study, we examined nestedness in moorland plant communities widely interspersed within the subalpine zone of northern Japan. Moorland sites differed in area (1000–160 000 m²) and were naturally isolated from one another to various extents within an inhospitable forest matrix. We also determined whether site characteristics (physical and morphometric measures) and species characteristics (niche position and breadth, based on species’ traits) are related to nestedness. Moorland plant communities in the study area were significantly nested. The pH and moorland kernel density (proxy for spatial clustering of moorlands around the focal site) were the most important predictors of moorland site nested rank in a nestedness matrix. Niche breadths of species (measured as variation in leaf mass area and height) predicted species’ nested ranks. Selective environmental tolerances imposed by environmental harshness and selective extinction caused by declines in site carrying capacities probably account for the nested subset pattern in moorland plant communities. The nested rank of species in the nestedness matrix can therefore be translated into the potential order of species loss explainable by species niche breadths (based on variation in functional traits). Complementary understanding of the determinants of site ranking and species ranking in the nestedness matrix provides powerful insight into ecological processes underlying nestedness and into the ways by which communities are assembled or disassembled by such processes.     

Nested assemblages of Orthoptera species in the Netherlands: the importance of habitat features and life-history traits

Aim Species communities often exhibit nestedness, the species found in species‐poor sites representing subsets of richer ones. In the Netherlands, where intensification of land use has led to severe fragmentation of nature, we examined the degree of nestedness in the distribution of Orthoptera species. An assessment was made of how environmental conditions and species life‐history traits are related to this pattern, and how variation in sampling intensity across sites may influence the observed degree of nestedness. Location The analysis includes a total of 178 semi‐natural sites in the Pleistocene sand region of the Netherlands. Methods A matrix recording the presence or absence of all Orthoptera species in each site was compiled using atlas data. Additionally, separate matrices were constructed for the species of suborders Ensifera and Caelifera. The degree of nestedness was measured using the binmatnest calculator. binmatnest uses an algorithm to sort the matrices to maximal nestedness. We used Spearman’s rank correlations to evaluate whether sites were sorted by area, isolation or habitat heterogeneity, and whether species were sorted by their dispersal ability, rate of development or degree of habitat specificity. Results We found the Orthoptera assemblages to be significantly nested. The rank correlation between site order and sampling intensity was high. The degree of nestedness was lower, but remained significant when under‐ and over‐sampled sites were excluded from the analysis. Site order was strongly correlated with both size of sample site and number of habitat types per site. Rank correlations showed that species were probably ordered by variation in habitat specificity, rather than by variation in dispersal capacity or rate of development of the species. Main conclusions Variation in sampling intensity among sites had a strong impact on the observed degree of nestedness. Nestedness in habitats may underlie the observed nestedness within the Orthoptera assemblages. Habitat heterogeneity is closely related to site area, which suggests that several large sites should be preserved, rather than many small sites. Furthermore, the results corroborate a focus of nature conservation policy on sites where rare species occur, as long as the full spectrum of habitat conditions and underlying ecological processes is secured.     

An evaluation of randomization models for nested species subsets analysis

Randomization models, often termed “null” models, have been widely used since the 1970s in studies of species community and biogeographic patterns. More recently they have been used to test for nested species subset patterns (or nestedness) among assemblages of species occupying spatially subdivided habitats, such as island archipelagoes and terrestrial habitat patches. Nestedness occurs when the species occupying small or species-poor sites have a strong tendency to form proper subsets of richer species assemblages. In this paper, we examine the ability of several published simulation models to detect, in an unbiased way, nested subset patterns from a simple matrix of site-by-species presence-absence data. Each approach attempts to build in biological realism by following the assumption that the ecological processes that generated the patterns observed in nature would, if they could be repeated many times over using the same species and landscape configuration, produce islands with the same number of species and species present on the same number of islands as observed. In mathematical terms, the mean marginal totals (column and row sums) of many simulated matrices would match those of the observed matrix. Results of model simulations suggest that the true probability of a species occupying any given site cannot be estimated unambiguously. Nearly all of the models tested were shown to bias simulation matrices toward low levels of nestedness, increasing the probability of a Type I statistical error. Further, desired marginal totals could be obtained only through ad-hoc manipulation of the calculated probabilities. Paradoxically, when such results are achieved, the model is shown to have little statistical power to detect nestedness. This is because nestedness is determined largely by the marginal totals of the matrix themselves, as suggested earlier by Wright and Reeves. We conclude that at the present time, the best null model for nested subset patterns may be one based on equal probabilities of occurrence for all species. Examples of such models are readily available in the literature. Received: 3 February 1997 / Accepted: 21 September 1997     

Effects of site and species characteristics on nested patterns of species composition in sedge meadows

Biotas of both geographical islands and habitat islands are often nested subsets of the biotas of successively more species-rich islands within the same system. The life history characteristics of a species may determine how that species contributes to the general pattern of species nestedness. Here, I investigate the floras of 56 sedge meadow wetlands in northern Illinois (USA) in order to characterize the degree of nestedness in these communities, determine which individual plant species contribute to the nested pattern, and investigate species characteristics that might be related to nonrandom patterns of distribution in individual plant species. The entire assemblage of species at all sedge meadows was significantly nested. Species richness and area were significantly correlated, and the nested pattern was closely related to site area, suggesting that species drop out of the assemblage in a predictable order as site area decreases. Some individual species exhibited nonrandom distributions across the sites, occurring more often in large, species-rich sites. Large sites were more likely than smaller sites to contain conservative species, i.e., those typical of pristine natural habitat, whereas nonconservative species were distributed more randomly among sites. Nested patterns of distribution of conservative species with respect to site area may result from their high probability of extinction on small sites or from a tendency for required habitats to co-occur on the same large sites. This revised version was published online in June 2006 with corrections to the Cover Date.     

The relationship between nested subsets,habitat subdivision,and species diversity

Biotic assemblages are said to be nested when the species making up relatively species-poor biotas comprise subsets of the species present at richer sites. Because species number and site area are often correlated, previous studies have suggested that nestedness may be relevant to questions of how habitat subdivision affects species diversity, particularly with respect to the question of whether a single large, contiguous patch of habitat will generally contain more species than collections of smaller patches having the same total combined area. However, inferences from analyses of nestedness are complicated by (1) variability in degrees of nestedness measured in natural communities, (2) variability in species-area relationships, and (3) the fact that nestedness statistics do not account for the size of habitat patches, only in the degree of overlap among sites with different numbers of species. By comparing various indices of nestedness with a saturation index that more directly measures the effect of habitat subdivision, it is shown that the first two of these factors are not as important as the third. Whether a single large site or several smaller ones having the same total combined area maximizes species diversity is dependent on (1) overlap in species composition among sites and (2) the number of species per unit area in the different sites. Because nestedness indices do not account for species number at a site, they cannot accurately predict how habitat subdivision affects species diversity patterns. Still, nestedness analyses are important in that they indicate the degree to which rare species tend to be found in the largest, or the most species-rich, sites, patterns not revealed by the saturation index. Both types of analysis are important in order to obtain a more complete picture of how species richness and compositional patterns are influenced by habitat subdivision.     

Can the biotic nestedness matrix be used predictively?

The biotas of a suite of neighboring patches of remnant vegetation often form a series of nested sub-sets, in which the species present in species-poor patches are non-random sub-sets of those present in richer patches. There has been recent interest in ways in which this knowledge may be used to aid conservation. We focus here on whether nested patterns can be used predictively. If nestedness in a fragmented system increases over time through biotic relaxation, locations where particular species may become extinct or are likely to colonize might be predictable and this could be useful in threatened-species management. We used the Temperature Calculator of Atmar and Patterson (1995) to arrange a matrix of bird species' occurrences in a series of buloke Allocasuarina leuhmannii woodland remnants so that nestedness was maximized. Probability bands generated by the calculator were used to predict possible colonization and extinction events. We then re-surveyed the avifauna of the fragments after a seven-year interval to test these predictions. Although nestedness increased between the two survey periods, there was no linear relationship between the generated probability of extinctions or colonizations and the accuracy of the predictions. The predictions derived from the calculator were no more accurate than a second set of predictions generated by use of a simple non-nested model. Despite the increase in nestedness, the arrangement of sites in each of the two maximally packed matrices was substantially different. For the nestedness matrix to generate accurate predictions, an increase in nestedness must be due to a minimization of unexpected species presences and absences rather than an extensive redistribution of species among remnants, as we found. The potential utility of nested patterns in predicting systematic colonization and extinction events should be further evaluated in other, less dynamic, fragmented systems such as those undergoing biotic relaxation.     

Temporal dynamics and nestedness of an oceanic island bird fauna

Aim To examine temporal variation in nestedness and whether nestedness patterns predict colonization, extinction and turnover across islands and species. Location Dahlak Archipelago, Red Sea. Method The distributions of land birds on 17 islands were recorded in two periods 30 years apart. Species and islands were reordered in the Nestedness Temperature Calculator, software for assessing degrees of nestedness in communities. The occupancy probability of each cell, i.e. species–island combinations, was calculated in the nested matrix and an extinction curve (boundary line) was specified. We tested whether historical and current nested ranks of species and islands were correlated, whether there was a relationship between occupancy probability (based on the historical data) and number of extinctions or colonizations (regression analyses) and whether the boundary line could predict extinctions and colonizations (chi‐square analyses). Results Historical and current nested ranks of islands and species were correlated but changes in occupancy patterns were common, particularly among bird species with intermediate incidence. Extinction and turnover of species were higher for small than large islands, and colonization was negatively related to isolation. As expected, colonizations were more frequent above than below the boundary line. Probability of extinction was highest at intermediate occupancy probability, giving a quadratic relationship between extinction and occupancy probability. Species turnover was related to the historical nested ranks of islands. Colonization was related negatively while extinction and occupancy turnover were related quadratically to historical nested ranks of species. Main conclusions Some patterns of the temporal dynamics agreed with expectations from nested patterns. However, the accuracy of the predictions may be confounded by regional dynamics and distributions of idiosyncratic, resource‐limited species. It is therefore necessary to combine nestedness analysis with adequate knowledge of the causal factors and ecology of targeted species to gain insight into the temporal dynamics of assemblages and for nestedness analyses to be helpful in conservation planning.     

Nestedness in fragmented landscapes: a case study on birds, arboreal marsupials and lizards

Aim The potential nestedness of assemblages of birds, arboreal marsupials and lizards was examined in a fragmented landscape in south‐eastern Australia. We assessed which ecological processes were related to the presence or absence of nestedness, particularly in relation to previous autoecological studies in the same study area. Location Data were collected at Buccleuch State Forest, c. 100 km to the west of the Australian Capital Territory in south‐eastern Australia. Methods Presence/absence matrices were compiled for birds (40 pine sites, 40 continuous forest sites, 43 fragments), arboreal marsupials (41 continuous forest sites, 39 fragments) and lizards (30 sites including all landscape elements) from a range of field surveys conducted since 1995. Nestedness was analysed using a standardized discrepancy measure, and statistical significance was assessed using the RANDNEST null model. For birds, species thought to be extinction‐prone were analysed separately to assess if assemblages comprising extinction‐prone species were more strongly nested than others. Also, sites with a substantial amount of Eucalyptus radiata were analysed separately to assess whether nestedness was stronger if environmental heterogeneity was minimized. Results The assemblages of lizards and arboreal marsupials were not nested, probably because of qualitative differences between species in response to environmental conditions. The assemblages of birds in fragments and pine sites were significantly nested, but nestedness was substantially stronger in fragments. For birds, nestedness appeared to be related to somewhat predictable extinction sequences, although there were many outliers in the analysis. Nestedness increased when extinction‐prone species were analysed by themselves. Nestedness decreased when environmental heterogeneity was minimized by including only sites dominated by E. radiata. Main conclusions In a given landscape, different vertebrate assemblages can respond in vastly different ways to fragmentation. Nestedness analyses can provide a useful overview of likely conservation issues in fragmented landscapes, for example by highlighting the possible roles of local extinction and immigration. However, nestedness analyses are a community‐level tool, and should be complemented by more detailed autoecological studies when applied in a conservation context.     

Differences in habitat quality explain nestedness in a land snail meta-community

We set up two alternative hypotheses on how environmental variables could foster nestedness; one of “nested habitats” and another of “nested habitat quality”. The former hypothesis refers to situations where the nestedness of species depends on a nestedness of discrete habitats. The latter considers situations where all species in an assemblage increase in abundance along the same environmental gradient, but differ in specialisation or tolerance. We tested whether litter‐dwelling land snails (terrestrial gastropods) in boreal riparian forest exhibited a nested community structure, whether such a pattern was related to differences in environmental variables among sites, and which of the two hypotheses that best could account for the found pattern. We sampled litter from 100 m² plots in 29 mature riparian forest sites along small streams in the boreal zone of Sweden. The number of snail species varied between 3 and 14 per site. Ranking the species‐by‐site matrix by PCA scores of the first ordination axis revealed a similarly significant nested pattern as when the matrix was sorted by number of species, showing that the species composition in this meta‐community can be properly described as nested. Several environmental variables, most notably pH index, were correlated with the first PCA axis. All but two species had positive eigenvectors in the PCA ordination and the abundance increased considerably along the gradient for most of the species implying that the hypothesis of “nested habitats” was rejected in favour of the “nested habitat quality” hypothesis. Analyses of nestedness have seldom been performed on equal sized plots, and our study shows the importance of understanding that variation in environmental variables among sites can result in nested communities. The conservation implications are different depending on which of our two hypotheses is supported; a conservation focus on species “hotspots” is more appropriate if the communities are nested because of “nested habitat quality”.     

Nestedness of desert bat assemblages: species composition patterns in insular and terrestrial landscapes

Nested patterns of community composition exist when species at depauperate sites are subsets of those occurring at sites with more species. Nested subset analysis provides a framework for analyzing species occurrences to determine non-random patterns in community composition and potentially identify mechanisms that may shape faunal assemblages. We examined nested subset structure of desert bat assemblages on 20 islands in the southern Gulf of California and at 27 sites along the Baja California peninsula coast, the presumable source pool for the insular faunas. Nested structure was analyzed using a conservative null model that accounts for expected variation in species richness and species incidence across sites (fixed row and column totals). Associations of nestedness and island traits, such as size and isolation, as well as species traits related to mobility, were assessed to determine the potential role of differential extinction and immigration abilities as mechanisms of nestedness. Bat faunas were significantly nested in both the insular and terrestrial landscape and island size was significantly correlated with nested structure, such that species on smaller islands tended to be subsets of species on larger islands, suggesting that differential extinction vulnerabilities may be important in shaping insular bat faunas. The role of species mobility and immigration abilities is less clearly associated with nestedness in this system. Nestedness in the terrestrial landscape is likely due to stochastic processes related to random placement of individuals and this may also influence nested patterns on islands, but additional data on abundances will be necessary to distinguish among these potential mechanisms.     

Nested subset patterns of species composition in a pond-dwelling fish fauna

Our objectives are to examine the influence of the difference in stress tolerance among species on patterns of nestedness and to test whether a set of several small ponds supports more species than a few large ponds of equal area. Although fish species assemblages for each group of all fish, tolerant and intolerant species were significantly nested, intolerant species showed stronger nested tendency than tolerant species, suggesting that the tolerance of species can influence the patterns of nestedness. These results suggest that the tolerance of species can influence the patterns of nestedness. As for the comparison of cumulative species richness in small ponds and large ponds, although small ponds supported more species for tolerant species, there was little difference for intolerant species.     

A comparative evaluation of pairwise nestedness measures

This paper deals with nestedness measures that are based on pairwise comparisons of sites, evaluates their performance and suggests improvements and generalizations. There are several conceptual and technical criteria to judge their ecological applicability. It is of primary concern whether the measures 1) have a clear mathematical definition, 2) are influenced by the ordering of the data matrix, 3) incorporate similarity alone or similarity together with a dissimilarity component, 4) consider site pairs with identical species number negatively or positively, 5) show sensitivity to small changes in the data, and 6) are not vulnerable to type I and type II error rates. We performed a detailed comparison of the nestedness metric based on overlap and decreasing fill (NODF), the percentage relativized nestedness and the percentage relativized strict nestedness functions (PRN and PRSN, respectively), based on analytical results as well as on artificial and actual examples. We show that NODF is in fact the average Simpson similarity of sites with different species totals, and that its value depends on how the matrix is actually ordered. NODF is modified to always produce the maximum possible result (NODF_max), independently of the order of columns and rows. Being based on similarities, NODF and NODF_max overemphasize the overlap component of nestedness and underrate richness difference which is also an important constituent of nested pattern in meta‐community data. This latter feature is reflected adequately by PRN and PRSN. However, PRSN is similar to NODF and NODF_max in sharing the disadvantages that 1) complete agreement and segregation in species composition are not distinguished, 2) a random matrix can have a higher value than truly nested patterns, and 3) they are ill‐conditioned statistically. These problems are rooted mostly in that site pairs with tied totals affect the result negatively. We emphasize that PRN is free from these difficulties. PRN, PRSN, and NODF_max, together with mean Simpson similarity exhibit highly similar statistical performance: they are resistant to type I and type II errors for the less constrained null models, although there are subtle differences depending on matrix fill and algorithm of randomization. The most constrained null model, with all marginal totals fixed, makes all statistics more sensitive to type I errors, although vulnerability depends greatly on matrix fill.     

BIODIVERSITY RESEARCH: Nestedness for different reasons: the distributions of birds,lizards and small mammals on islands of an inundated lake

Aim We examined whether the community compositions of birds, lizards and small mammals were nested in a fragmented landscape in the Thousand Island Lake, China. We also assessed whether the mechanisms influencing nestedness differed among these taxonomic groups. Location Thousand Island Lake, China. Methods Presence/absence matrices were compiled for birds (42 islands) and lizards (42 islands) using line‐transect methods, and for small mammals (14 islands) using live‐trapping methods from 2006 to 2009. Nestedness was analysed using BINMATNEST, and statistical significance was assessed using the conservative null model 3. We used Spearman rank correlations and partial Spearman rank correlations to examine associations of nestedness and habitat variables (area, isolation, habitat diversity and plant richness) as well as life‐history traits (body size, habitat specificity, geographical range size and area requirement) related to species extinction and immigration tendencies. Results The community compositions of birds, lizards and small mammals were all significantly nested, but the causal factors underlying nestedness differed among taxonomic groups. For birds, island area, habitat specificity and area requirement were significantly correlated with nestedness after controlling for other independent variables. For lizards, habitat heterogeneity was the single best correlate of nestedness. For small mammals, island area, habitat heterogeneity and habitat specificity were significantly correlated with nestedness. The nested patterns of birds, lizards and small mammals were not attributable to passive sampling or selective colonization. Main conclusions The processes influencing nested patterns differed among taxonomic groups. Nestedness of bird assemblages was driven by selective extinction, and lizard assemblage was caused by habitat nestedness, while nestedness of small mammals resulted from both selective extinction and habitat nestedness. Therefore, we should take taxonomic differences into account when analysing nestedness to develop conservation guidelines and refrain from using single taxa as surrogates for others.     

A consistent metric for nestedness analysis in ecological systems: reconciling concept and measurement

Nestedness has been widely reported for both metacommunities and networks of interacting species. Even though the concept of this ecological pattern has been well-defined, there are several metrics by which it can be quantified. We noted that current metrics do not correctly quantify two major properties of nestedness: (1) whether marginal totals (i.e. fills) differ among columns and/or among rows, and (2) whether the presences (1's) in less-filled columns and rows coincide, respectively, with those found in the more-filled columns and rows. We propose a new metric directly based on these properties and compare its behavior with that of the most used metrics, using a set of model matrices ranging from highly-nested to alternative structures in which no nestedness should be detected. We also used an empirical dataset to explore possible biases generated by the metrics as well as to evaluate correlations between metrics. We found that nestedness has been quantified by metrics that inappropriately detect this pattern, even for matrices in which there is no nestedness. In addition, the most used metrics are prone to type I statistical errors while our new metric has better statistical properties and consistently rejects a nested pattern for different types of random matrices. The analysis of the empirical data showed that two nestedness metrics, matrix temperature and the discrepancy measure, tend to overestimate the degrees of nestedness in metacommunities. We emphasize and discuss some implications of these biases for the theoretical understanding of the processes shaping species interaction networks and metacommunity structure.